Project 001: Tiered Skirt Variations
Let's explore how to draft a tiered skirt with 2 or 5 tiers.
Hello sew-friends! And welcome to all 935+ subscribers! It warms my heart that so many people have signed up to learn more about sewing and math and I hope that you've been enjoying this series so far. Today, I'm going to share some design variations on the tiers of the skirt.
Last week, I showed you how to draft a three-tiered skirt that has proportions of .75x, x and 1.5x. But there are infinitely many ways to design a tiered skirt. If you want to play around and design your own proportions, I found that sketching on lined paper and graph paper was an easy way to compare proportions of the tiers.
Today, I'm going to show you how to draft a two different two tier skirts and a five tier skirt. You can probably guess that the more tiers there are, the more complicated the math is. That said, this process is very similar to my last post, where I showed how to draft a three tier skirt. (In fact, calculating the width and length of the waistband pattern piece is the same for all variations and is covered in previous posts.)
For all of the skirts, the width of the tiers is determined by the finished circumference and the gathers multiplier. For the lengths, we look at the design proportions of the tiers, the finished length "B", and then find an expression for the "X" height of the skirt.
If you haven't read my last post yet, I recommend starting there. You will want to check out the worksheet and the measurements that the different letters represent.
How to Draft a Two Tier Skirt
For this first design, we will draft two tiers, a long one at the top that is "2X" (or twice as) long and a short bottom tier that is the length of "X".
First, we solve for “X” by comparing the final skirt length “B” to the sum of its parts.
B = E + F + 2X + X
(Now, we simplify to solve for "x". First, subtract E and F from both sides.)
B−E−F = 2X + X
(Then, add up the "X" values on the right side of the equation.)
B−E−F = 3X
(Finally, divide both sides by 3.)
(B−E−F)/3 = X
Now we can calculate the length of the tiers. The length of Tier 1 is 2 times the "X" height plus the seam allowance “G” on each side.
Tier 1 Length 2×((B−E−F)/3 + G×2
Tier 2 is equal to the "X" height plus the seam allowance “G” at the top and hem allowance “H” at the bottom.
Tier 2 Length (B−E−F)/3) + G + H
Bonus variation! What if you want a short tier at the top and a long tier at the bottom? I’ve seen this design a lot and I think it’s pretty cool. For this design proportion, I made Tier 1 equal the "X" height and Tier 2 equal "3X". See formulas in the graphic above or written out below.
First, we solve for “X” by comparing the final skirt length “B” to the sum of its parts.
B = E + F + X + 3X
(Now, we simplify to solve for "X". First, subtract E and F from both sides.)
B−E−F = X + 3X
(Then, add up the "X" values on the right side of the equation.)
B−E−F = 4X
(Finally, divide both sides by 4.)
(B−E−F)/4 = X
Now we can calculate the length of the tiers. The length of Tier 1 is the "X" height plus the seam allowance “G” on each side. So that length is represented by
Tier 1 Length (B−E−F)/4 + G×2
Tier 2 is 3 times the "X" height plus the seam allowance “G” at the top and hem allowance “H” at the bottom.
Tier 2 Length 3×((B−E−F)/4) + G + H
The widths of the tiers are calculated the same for both designs. That said, for the skirt with a longer first tier, you might want to add more ease (around 6”) to allow freer movement for walking.
For the widths of the tiers, we follow the same approach as the last lesson. The second tier will be wider than the first tier by a factor of "D", the gathers multiplier. And, we will use the expression (A + C)/2 to represent half the finished circumference of the skirt at the hip.
The Waistband and Tier 1 have the same width. It is (A + C)/2 + G×2. This is the finished width plus seam allowance.
To calculate Tier 2, we multiply our starting expression by “D” Gathers Multiplier. That formula is, D×((A + C)/2) + G×2.
How to Draft a Five Tier Skirt
This draft is a little more complicated. For this design, each tier is just a smidge longer than the one above. I found a factor of 120% to be visually pleasing for five tiers. Each tier is successively wider and taller than the above so to simplify the formulas I'm using powers, i.e. "Y" to the 3rd power meaning Y times Y times Y or Y×Y×Y.
For the lengths of the Five Tier Skirt, we'll start by looking at the design proportions and finished length "B" and find an expression for the "X" height of the skirt.
B = E + F + X*1.2 + X*(1.2)^2 + X*(1.2)^3 + X*(1.2)^4
(Now, we simplify to solve for "x". First, subtract E and F from both sides.)
B−E−F = X*1.2 + X*(1.2)^2 + X*(1.2)^3 + X*(1.2)^4
(Add up the "X" values on the right side. Here, I rounded up to 6.5.)
B−E−F = 6.5X
(Finally, divide both sides by 6.5.)
(B−E−F)/6.5 = X
The length of Tier 1 is "x" height plus the seam allowance “G” at the top and bottom.
Tier 1 Length (B−E−F)/6.5 + G×2
For each successive tier, we multiply by 1.2 an additional time.
Tier 2 Length 1.2×(B−E−F)/6.5 + G×2
Tier 3 Length 1.2×1.2×(B−E−F)/6.5 + G×2
Tier 4 Length 1.2×1.2×1.2×(B−E−F)/6.5 + G×2
Finally, Tier 5 is 1.2^4 times the "x" height plus the seam allowance at the top and hem allowance at the bottom.
Tier 5 Length 1.2×1.2×1.2×1.2×(B−E−F)/6.5 + G + H
Let's calculate the widths. Just like last week, we'll use (A+C)/2, half the finished circumference at the hip, as the basis for calculating each tier. For each new tier, we will multiply by "D" (the gathers multiplier) one more time, so that each tier is proportionally wider. (You might be inclined to multiply by 2D, 3D, 4D but that will make the tiers too wide. Our multiplier “D” should be something like 1.2. So, multiplying DxD = D^2= 1.2 x 1.2 = 1.44. Likewise DxDxD = D^3 = 1.2 x 1.2 x 1.2 = 1.728.)
Note: For this five tier skirt, I recommend using a smaller gathers multiplier so that the tiers don't get too wide or too heavy.
Again, the Waistband and Tier 1 have the same width. It is (A + C)/2 + G×2, our finished circumference plus seam allowance for each side of the pattern piece.
To calculate Tier 2, we multiply our starting expression by D Gathers Multiplier. That formula is, D×((A + C)/2) + G×2.
To calculate Tier 3, we multiply by D again and then add the seam allowance. That formula is, D×D×((A + C)/2) + G×2 = D^2×((A + C)/2) + G×2
To calculate Tier 4, we multiply by D again and then add the seam allowance. That formula is, D×D×D×((A + C)/2) + G×2 = D^3×((A + C)/2) + G×2
To calculate Tier 5, we multiply by D again and then add the seam allowance. That formula is, D×D×D×D×((A + C)/2) + G×2 = D^4×((A + C)/2) + G×2
One of the best things about sewing and about designing your own patterns is that you can customize in so many ways. Here are a few more ideas for how to customize the design of your skirt.
Ideas for customizing the design of your skirt
Number of tiers
Proportion of tiers
Percentage of gathers
Style of waistband (In Exercise 1, I talked about adding ease to the waistband to create a paper bag style. You can also use topstitching to create a different look.)
Add a drawstring at the waist
Add patch pockets or in-seam pockets
Add decorative trim to the bottom edge of the tiers
Thank you so much for following along with this project. I hope that you enjoyed this post! The next couple of weeks will be more journal style as I get ready for our next project. Please let me know in the comments if you have any questions or feedback.
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Happy mathing!
Beth
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